Question

Leslie is interested in testing whether the performance of girls and boys on a standardized math test differs. Contrary to the stereotype she believes that young girls are better at math then boys and the resulting differences in young adults is due to social stigma. To test this, she collects data from 63 girls and 51 boys who were randomly selected from a local elementary school. She decides to perform a two-tailed test as this is the standard and uses a more conservative alpha of .0 The mean score for girls is 76 (s=13), and the mean score for boys is 71 (s=8). Perform the 4 steps of hypothesis testing if s_M1-M2 = 2.08.

Answer 1

Let x = Girls and y = Boys

Given   = 63 and   = 51

Given Means are

= 76 and = 71

Given Standard Deviations are

= 13

= 8

Therefore = 169 and = 64

We fram Null Hypothesis as

: M1-M2 = 2.08.

(Or)

: There is no significant difference between the performance of girls and boys on a standardized math test.

To Test the we use the Z - Statistic ( Since the given samples are large)

We Compare with and we draw our conclusion.

If       ; we Accepth at 5% Level of Significant

If     ; we Reject at 5% Level of Significant

NOTE: Since is not specified here, so we can =5% = 0.05

Now

Since ; So, we Reject at 5% Level of Significant

Therefore we conclude that " There is significant difference between the performance of girls and boys on a standardized math test",

(Or)

M1-M2 Not equal to 2.08.

NOTE:

NOTE: To See the Critical Values of Z; we use the Standard Normal area tabulated values which i posted below.

How to see?

If alpha = 5% the confidence interval = 95%

Divide the value 95 with 100. you will get 0.95 and after that divide the value 0.95 with 2; you will get 0.475. Now Search this 0.475 in side the table ( repeating again see inside the table). You will find this at the intersection of (1.9, 0,06) which is Zcri value i.e 1.96.

Like this you can find the Zcri for any alpha values.